Averages – Hard Level Questions – UGC NET Paper 1

Q1): The average of 10 numbers is 42. One number is replaced by 58 and the new average becomes 45. What was the replaced number?
A) 26
B) 28
C) 30
D) 32

Answer: B) 28

Explanation:

  • Step 1: Old sum = 42 × 10 = 420
  • Step 2: New sum = 45 × 10 = 450
  • Step 3: Increase in sum = 450 − 420 = 30
  • Step 4: Replacement change = 58 − x = 30 ⇒ x = 28
  • Final: Option B is correct

Q2): The average of 15 numbers is 28. The average of the first 9 numbers is 25 and the average of the last 5 numbers is 34. Find the 10th number.
A) 23
B) 24
C) 25
D) 26

Answer: C) 25

Explanation:

  • Step 1: Total sum of 15 numbers = 28 × 15 = 420
  • Step 2: Sum of first 9 numbers = 25 × 9 = 225
  • Step 3: Sum of last 5 numbers = 34 × 5 = 170
  • Step 4: 10th number = 420 − (225 + 170) = 25
  • Final: Option C is correct

Q3): The average of 9 numbers is 30. The average of the first 4 numbers is 24 and the average of the next 2 numbers is 33. The remaining 3 numbers are in the ratio 2 : 3 : 4. Find the largest of the remaining 3 numbers.
A) 44
B) 46
C) 48
D) 50

Answer: C) 48

Explanation:

  • Step 1: Total sum of 9 numbers = 30 × 9 = 270
  • Step 2: Sum of first 4 = 24 × 4 = 96
  • Step 3: Sum of next 2 = 33 × 2 = 66
  • Step 4: Sum of remaining 3 = 270 − (96 + 66) = 108
  • Step 5: Ratio sum = 2 + 3 + 4 = 9 ⇒ each part = 108 ÷ 9 = 12
  • Step 6: Numbers = 24, 36, 48 ⇒ largest = 48
  • Final: Option C is correct

Q4): The average of 20 people is 35. When 5 new people join, the average becomes 37. What is the average age of the 5 new people?
A) 41
B) 43
C) 45
D) 47

Answer: C) 45

Explanation:

  • Step 1: Old total = 35 × 20 = 700
  • Step 2: New total = 37 × 25 = 925
  • Step 3: Total age of 5 new people = 925 − 700 = 225
  • Step 4: Average of new people = 225 ÷ 5 = 45
  • Final: Option C is correct

Q5): Group A has 30 students with average 48. Group B has average 60. If the combined average is 52, how many students are in Group B?
A) 10
B) 12
C) 15
D) 18

Answer: C) 15

Explanation:

  • Step 1: Let students in B = n
  • Step 2: Total marks = (30×48) + (n×60)
  • Step 3: Combined average: (1440 + 60n) ÷ (30 + n) = 52
  • Step 4: 1440 + 60n = 1560 + 52n ⇒ 8n = 120 ⇒ n = 15
  • Final: Option C is correct

Q6): The average of 7 consecutive integers is 32. Find the product of the smallest and the largest integer.
A) 1008
B) 1015
C) 1024
D) 1035

Answer: B) 1015

Explanation:

  • Step 1: For 7 consecutive integers, the middle number = average
  • Step 2: Middle = 32 ⇒ numbers are 29, 30, 31, 32, 33, 34, 35
  • Step 3: Smallest = 29, largest = 35
  • Step 4: Product = 29 × 35 = 1015
  • Final: Option B is correct

Q7): The average of three numbers is 20. The average of the first two numbers is 15 and the average of the last two numbers is 25. What is the greatest number?
A) 35
B) 38
C) 40
D) 42

Answer: C) 40

Explanation:

  • Step 1: Let numbers be x, y, z
  • Step 2: (x + y)/2 = 15 ⇒ x + y = 30
  • Step 3: (y + z)/2 = 25 ⇒ y + z = 50
  • Step 4: (x + y + z)/3 = 20 ⇒ x + y + z = 60
  • Step 5: From (x+y+z) − (x+y): z = 60 − 30 = 30
  • Step 6: From (y+z) = 50 ⇒ y = 20 ⇒ x = 10 ⇒ greatest = 30?
  • Final: Option A? (Check options)

Correction (Final Answer): A) 30

Explanation (Corrected):

  • Step 1: x + y = 30
  • Step 2: y + z = 50
  • Step 3: x + y + z = 60
  • Step 4: z = 60 − 30 = 30
  • Step 5: y = 50 − 30 = 20, x = 30 − 20 = 10
  • Final: Greatest number = 30, so Option A is correct

Q8): The average of the first 3 numbers is 20 and the average of the next 3 numbers is 30. What is the overall average of all 6 numbers if the first 3 are increased by 10% and the next 3 are increased by 20%?
A) 28
B) 29
C) 30
D) 31

Answer: B) 29

Explanation:

  • Step 1: Sum of first 3 = 20 × 3 = 60
  • Step 2: Sum of next 3 = 30 × 3 = 90
  • Step 3: New first-sum = 60 × 1.10 = 66
  • Step 4: New second-sum = 90 × 1.20 = 108
  • Step 5: New total = 66 + 108 = 174 ⇒ new average = 174 ÷ 6 = 29
  • Final: Option B is correct

Q9): In a course, Theory (50%), Practical (30%), Viva (20%). A student scored 68 in Theory and 80 in Practical. What must be the Viva score to get overall 72?
A) 68
B) 70
C) 72
D) 74

Answer: B) 70

Explanation:

  • Step 1: Weighted average = 0.50T + 0.30P + 0.20V
  • Step 2: Put values: 72 = 0.50×68 + 0.30×80 + 0.20V
  • Step 3: 0.50×68 = 34 and 0.30×80 = 24 ⇒ total = 58
  • Step 4: 72 = 58 + 0.20V ⇒ 0.20V = 14 ⇒ V = 70
  • Final: Option B is correct

Q10): A person covers 1/3 of a distance at 30 km/h and the remaining 2/3 at 45 km/h. Find the average speed for the whole trip.
A) 38.0 km/h
B) 38.6 km/h
C) 39.0 km/h
D) 40.0 km/h

Answer: B) 38.6 km/h

Explanation:

  • Step 1: Assume total distance = 3d (so 1/3 = d and 2/3 = 2d)
  • Step 2: Time₁ = d/30, Time₂ = 2d/45
  • Step 3: Total time = d/30 + 2d/45 = (3d/90) + (4d/90) = 7d/90
  • Step 4: Average speed = Total distance / Total time = 3d ÷ (7d/90) = 270/7
  • Step 5: 270/7 ≈ 38.6 km/h
  • Final: Option B is correct

Q11): The average of 11 numbers is 50. If one number is excluded, the average of the remaining 10 numbers becomes 47. Find the excluded number.
A) 77
B) 79
C) 80
D) 83

Answer: C) 80

Explanation:

  • Step 1: Total sum of 11 numbers = 50 × 11 = 550
  • Step 2: Sum of remaining 10 numbers = 47 × 10 = 470
  • Step 3: Excluded number = 550 − 470 = 80
  • Step 4: Match with options
  • Final: Option C is correct

Q12): The average of 12 matches is 35. After removing the highest score and the lowest score, the average of the remaining 10 matches is 34. If the highest score is 60, find the lowest score.
A) 18
B) 20
C) 22
D) 24

Answer: B) 20

Explanation:

  • Step 1: Total of 12 matches = 35 × 12 = 420
  • Step 2: Total of remaining 10 matches = 34 × 10 = 340
  • Step 3: Highest + lowest = 420 − 340 = 80
  • Step 4: Lowest = 80 − 60 = 20
  • Final: Option B is correct

Q13): A team has average age 24. Three players with average age 20 are replaced by two players with average age 30. New average becomes 24.5. Find the original team size.
A) 45
B) 49
C) 50
D) 52

Answer: B) 49

Explanation:

  • Step 1: Let original team size = n ⇒ original total age = 24n
  • Step 2: Remove 3 players (avg 20) ⇒ subtract 3×20 = 60
  • Step 3: Add 2 players (avg 30) ⇒ add 2×30 = 60
  • Step 4: Net change in total = −60 + 60 = 0 ⇒ new total = 24n
  • Step 5: New size = n − 1, new average = 24n ÷ (n − 1) = 24.5
  • Step 6: 24n = 24.5(n − 1) ⇒ 24n = 24.5n − 24.5 ⇒ 0.5n = 24.5 ⇒ n = 49
  • Final: Option B is correct

Q14): Five numbers are in the ratio 2 : 3 : 4 : 5 : 6 and their average is 28. Find the difference between the largest and smallest number.
A) 21
B) 24
C) 28
D) 30

Answer: C) 28

Explanation:

  • Step 1: Let numbers be 2k, 3k, 4k, 5k, 6k
  • Step 2: Sum = (2+3+4+5+6)k = 20k
  • Step 3: Average = 20k ÷ 5 = 4k
  • Step 4: 4k = 28 ⇒ k = 7
  • Step 5: Largest − smallest = 6k − 2k = 4k = 28
  • Final: Option C is correct

Q15): The average of 9 numbers is 32. If removing one number decreases the average by 1.5, find the removed number.
A) 42
B) 44
C) 46
D) 48

Answer: B) 44

Explanation:

  • Step 1: Old sum = 32 × 9 = 288
  • Step 2: New average = 32 − 1.5 = 30.5
  • Step 3: New sum (8 numbers) = 30.5 × 8 = 244
  • Step 4: Removed number = 288 − 244 = 44
  • Final: Option B is correct

Q16): The average of A and B is 30. The average of B and C is 35. The average of A, B and C is 33. Find the value of B.
A) 30
B) 31
C) 32
D) 34

Answer: B) 31

Explanation:

  • Step 1: (A + B)/2 = 30 ⇒ A + B = 60
  • Step 2: (B + C)/2 = 35 ⇒ B + C = 70
  • Step 3: (A + B + C)/3 = 33 ⇒ A + B + C = 99
  • Step 4: Add Step 1 and Step 2: A + 2B + C = 130
  • Step 5: Subtract Step 3: (A + 2B + C) − (A + B + C) = 130 − 99
  • Step 6: B = 31
  • Final: Option B is correct

Q17): The average of 12 tests is 75. After rechecking, one test score is corrected from 68 to 83. What is the new average?
A) 75.75
B) 76.00
C) 76.25
D) 76.50

Answer: C) 76.25

Explanation:

  • Step 1: Old total = 75 × 12 = 900
  • Step 2: Score increases by 83 − 68 = 15
  • Step 3: New total = 900 + 15 = 915
  • Step 4: New average = 915 ÷ 12 = 76.25
  • Final: Option C is correct

Q18): The average sales for 7 days is recorded as ₹2500 per day. Later it is found that one day’s sales was written as ₹3400 instead of ₹4300. What is the correct average sales?
A) ₹2600.00
B) ₹2628.57
C) ₹2650.00
D) ₹2700.00

Answer: B) ₹2628.57

Explanation:

  • Step 1: Recorded total for 7 days = 2500 × 7 = 17500
  • Step 2: Error = 4300 − 3400 = 900 (total should increase by 900)
  • Step 3: Correct total = 17500 + 900 = 18400
  • Step 4: Correct average = 18400 ÷ 7 = 2628.57 (approx)
  • Final: Option B is correct

Q19): The average of 5 numbers is 40. If the first two numbers are doubled and the last three numbers are halved, the new average becomes 44. Find the sum of the first two numbers.
A) 78
B) 80
C) 82
D) 84

Answer: B) 80

Explanation:

  • Step 1: Let sum of first two = S and sum of last three = T
  • Step 2: Original total = 40 × 5 = 200 ⇒ S + T = 200
  • Step 3: New total = 44 × 5 = 220
  • Step 4: New total equation: 2S + (T/2) = 220
  • Step 5: Multiply by 2: 4S + T = 440
  • Step 6: Put T = 200 − S ⇒ 4S + (200 − S) = 440 ⇒ 3S = 240 ⇒ S = 80
  • Final: Option B is correct

Q20): The average of 6 numbers is 17. One number is equal to 2/3 of the average of the remaining 5 numbers. Find that number.
A) 10
B) 12
C) 14
D) 16

Answer: B) 12

Explanation:

  • Step 1: Total of 6 numbers = 17 × 6 = 102
  • Step 2: Let the special number be x ⇒ sum of remaining 5 = 102 − x
  • Step 3: Average of remaining 5 = (102 − x)/5
  • Step 4: Given x = (2/3) × [(102 − x)/5]
  • Step 5: 15x = 2(102 − x) ⇒ 15x = 204 − 2x ⇒ 17x = 204
  • Step 6: x = 204/17 = 12
  • Final: Option B is correct

This Tutorial is Related to: Aptitude Mcqs, Arithmetic Mean, Average Speed, Averages, Averages Questions, Change In Average, Combined Average, Hard Level, Missing Number Average, Pyq Pattern, Ratio And Average, Replacement Problems, Ugc Net Paper 1, Unit 5, Weighted Average

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